# Kneser-type theorem for the Darboux problem in Banach spaces

Mieczysław Cichoń; Ireneusz Kubiaczyk

Commentationes Mathematicae Universitatis Carolinae (2001)

- Volume: 42, Issue: 2, page 267-279
- ISSN: 0010-2628

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topCichoń, Mieczysław, and Kubiaczyk, Ireneusz. "Kneser-type theorem for the Darboux problem in Banach spaces." Commentationes Mathematicae Universitatis Carolinae 42.2 (2001): 267-279. <http://eudml.org/doc/248780>.

@article{Cichoń2001,

abstract = {In this paper we study the Darboux problem in some class of Banach spaces. The right-hand side of this problem is a Pettis-integrable function satisfying some conditions expressed in terms of measures of weak noncompactness. We prove that the set of all local pseudo-solutions of our problem is nonempty, compact and connected in the space of continuous functions equipped with the weak topology.},

author = {Cichoń, Mieczysław, Kubiaczyk, Ireneusz},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {Pettis integral; Fubini theorem; Darboux problem; measure of weak noncompactness; Pettis integral; Fubini theorem; Darboux problem; measure of weak noncompactness},

language = {eng},

number = {2},

pages = {267-279},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Kneser-type theorem for the Darboux problem in Banach spaces},

url = {http://eudml.org/doc/248780},

volume = {42},

year = {2001},

}

TY - JOUR

AU - Cichoń, Mieczysław

AU - Kubiaczyk, Ireneusz

TI - Kneser-type theorem for the Darboux problem in Banach spaces

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2001

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 42

IS - 2

SP - 267

EP - 279

AB - In this paper we study the Darboux problem in some class of Banach spaces. The right-hand side of this problem is a Pettis-integrable function satisfying some conditions expressed in terms of measures of weak noncompactness. We prove that the set of all local pseudo-solutions of our problem is nonempty, compact and connected in the space of continuous functions equipped with the weak topology.

LA - eng

KW - Pettis integral; Fubini theorem; Darboux problem; measure of weak noncompactness; Pettis integral; Fubini theorem; Darboux problem; measure of weak noncompactness

UR - http://eudml.org/doc/248780

ER -

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